A342708 - OEIS

A342708

Triangle read by rows with n >= 1, 0 <= k <= n-1: in general T(n,k) = T(n-1,k-1) - T(n-k,k), except T(1,0)=1, T(n,0)=0 for n>=2; T(n,k) = 0 for k>=n.

1, 0, 1, 0, -1, 1, 0, 1, -1, 1, 0, -1, 0, -1, 1, 0, 1, 0, 0, -1, 1, 0, -1, 1, -1, 0, -1, 1, 0, 1, -1, 2, -1, 0, -1, 1, 0, -1, 0, -1, 1, -1, 0, -1, 1, 0, 1, 0, 1, 0, 1, -1, 0, -1, 1, 0, -1, 1, -2, 1, -1, 1, -1, 0, -1, 1, 0, 1, -1, 2, -1, 2, -1, 1, -1, 0, -1, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,32

COMMENTS

Absolute value of sum of triangle array rows = A000700.

Sum of absolute value of each number in a row = absolute value of A000025.

Triangle recurrence is the same as A008284 (row sums equal A000041) except instead of adding the two pieces for the corresponding output a subtraction is performed.

LINKS

Joe Michelson, Table of n, a(n) for n = 1..11628 (first 152 rows)

EXAMPLE

The triangle begins:

n\k| 0 1 2 3 4 5 6 7 8 9 10 11 ...

---+--------------------------------------------------

1 | 1;

2 | 0, 1;

3 | 0, -1, 1;

4 | 0, 1, -1, 1;

5 | 0, -1, 0, -1, 1;

6 | 0, 1, 0, 0, -1, 1;